Obtaining the Strength of the Magnetic Field from E- and B-Modes of Dust Polarization

We perform numerical simulations of supersonic magnetohydrodynamic (MHD) turbulence and calculate Fourier power spectra of E- and B-modes arising from dust polarization. We pay close attention to the ratio of E-mode to B-mode spectra (a.k.a. E/B power asymmetry) on small spatial scales. We find that the ratio depends on the strength of the mean magnetic field: the stronger the mean magnetic field, the smaller the ratio. More precisely speaking, the ratio scales with the Alfvén Mach number M _A , the rms velocity divided by the Alfvén speed of the mean magnetic field, when it lies in the range 1 ≲ M _A ≲ 30. This result implies that we can use the E/B power asymmetry to constrain the strength of the mean magnetic field in supersonic and super-Alfvénic MHD turbulence.